# The relationship between Stress-Energy tensor and Mass

1. Dec 9, 2012

### ShayanJ

In Einstein field equations,the term that is responsible for curving Space-Time is the Stress-Energy tensor.But we know that mass should be able to curve space-time.So I think every mass distribution should have a Stress-Energy tensor associated with it.
What is that relationship?
Thanks

2. Dec 9, 2012

### dextercioby

Volumic mass density is the 00 component of the stress-energy tensor.

3. Dec 9, 2012

### stevendaryl

Staff Emeritus
The relationship is explained in Wikipedia here: http://en.wikipedia.org/wiki/Stressâ€“energy_tensor

The simplest case is a perfect fluid at rest. In that case, the nonzero components of the stress-energy tensor $T^{\alpha \beta}$ are:
$T^{0 0} = \rho$, where $rho$ is the mass-energy density, and
$T^{1 1} = T^{2 2} = T^{3 3} = p$, where $p$ is the pressure.

4. Dec 9, 2012

### K^2

Energy density, which is proportional to mass density only for a body at rest.

5. Dec 9, 2012

### ShayanJ

Thanks guys
But what about other components?

6. Dec 12, 2012

### stevendaryl

Staff Emeritus
As I said, for a fluid at rest, the three spatial components of the stress-energy tensor are just the pressure.

7. Dec 12, 2012

### Staff: Mentor

The diagram on the Wikipedia page identifies what the various components (or groups of them) represent.

8. Dec 12, 2012

### cosmik debris

In addition to what Steven said, the off diagonal terms are shear stresses.

9. Dec 12, 2012

### pervect

Staff Emeritus
And of course you have momentum density....if you have a moving object or fluid.